np.eye() for identity matrices in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.eye() with default parameters

What is the output of this code snippet?

import numpy as np
print(np.eye(3))

NumPy

import numpy as np
print(np.eye(3))

A

[[0. 1. 0.]
 [1. 0. 1.]
 [0. 1. 0.]]

B

[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

C

[[1 0 0]
 [0 1 0]
 [0 0 1]]

D

[[0. 0. 0.]
 [0. 0. 0.]
 [0. 0. 0.]]

💡 Hint

np.eye(n) creates an n x n matrix with 1s on the main diagonal and 0s elsewhere.

np.eye(3) creates a 3x3 identity matrix with 1.0 on the diagonal and 0.0 elsewhere.

❓ Predict Output

intermediate

Effect of k parameter in np.eye()

What is the output of this code?

import numpy as np
print(np.eye(4, k=1))

NumPy

import numpy as np
print(np.eye(4, k=1))

A

[[0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]
 [0. 0. 0. 0.]]

B

[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]

C

[[0. 0. 0. 0.]
 [1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]

D

[[0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [1. 0. 0. 0.]]

💡 Hint

The k parameter shifts the diagonal by k positions above (positive) or below (negative) the main diagonal.

k=1 shifts the diagonal of 1s one step above the main diagonal, so the 1s appear just above the main diagonal.

❓ data_output

advanced

Shape of np.eye() with different rows and columns

What is the shape of the array created by this code?

import numpy as np
arr = np.eye(3, 5)
print(arr.shape)

NumPy

import numpy as np
arr = np.eye(3, 5)
print(arr.shape)

A (5, 3)

B (5, 5)

C (3, 5)

D (3, 3)

💡 Hint

The first argument is the number of rows, the second is the number of columns.

np.eye(3, 5) creates a matrix with 3 rows and 5 columns, so the shape is (3, 5).

❓ visualization

advanced

Visual pattern of np.eye() with negative k

Which option shows the correct printed output of this code?

import numpy as np
print(np.eye(4, k=-1))

NumPy

import numpy as np
print(np.eye(4, k=-1))

A

[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]

B

[[0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]
 [0. 0. 0. 0.]]

C

[[0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [0. 0. 0. 0.]
 [1. 0. 0. 0.]]

D

[[0. 0. 0. 0.]
 [1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]

💡 Hint

Negative k shifts the diagonal below the main diagonal.

k=-1 places 1s on the diagonal just below the main diagonal, so the 1s start at position (1,0).

🧠 Conceptual

expert

Understanding dtype effect in np.eye()

What will be the dtype and output of this code?

import numpy as np
arr = np.eye(2, dtype=int)
print(arr)
print(arr.dtype)

NumPy

import numpy as np
arr = np.eye(2, dtype=int)
print(arr)
print(arr.dtype)

A

[[1 0]
 [0 1]]
int64

B

[[1 0]
 [0 1]]
float64

C

[[1. 0.]
 [0. 1.]]
float64

D

[[1. 0.]
 [0. 1.]]
int32

💡 Hint

dtype=int forces the matrix elements to be integers instead of floats.

np.eye with dtype=int creates an integer identity matrix. The default int type on many systems is int64.